Antenna pattern synthesizer



||t66 l I Feb. 17, 1959 G. STM/1S :2,874,381

. ANTENNA PATTERN SYNTI-IESIZER FiledSept. 25, 1956 2 Sheets-Sheet l V f :f l I l l Snucntor 60S @7797/6 (lttorneg 2 Sheets-Sheet 2 Feb. 17, 1959 G. sTAvls ANTENNA PATTERN SYNTHESTZER Filed Sept. 25, 1956 United States Patent O M ANTENNA PATTERN sYNTHEsIzER Gus Stayis, Ossining, N. Y., assignor to General Precision Laboratory Incorporated, a corporation of New York Application September 25, 1956, Serial No.` 611,898

Claims. (Cl. 343-703) `This invention relates to apparatus for synthesizing and displaying the radiation pattern of a linear array antenna. Linear array antennas composed of isotropic radiating elements emit energy in one or more 'cones the axes of which coincide with the axis of the array. At the present time the most widely used class of linear arrays is that class in which the spacing between elements is uniform and in which the phase of the energy emitted progresses uniformly `from element to element.. All linear array antennas of this .class have a basic radiation pattern comprising a number of lmajor lobes for which the radiation from al1 the elements combines in phase and a number of minor lobes of smaller amplitudes between the major lobes. Variation of the spacing between elements varies the number of lobes (both major and minor) while variation in the phase progression shifts the angle at which the lobes appear.

The radiation patterns of linear arrays having uniform spacing and phase progression are well known' to those skilled in the art. However, the patterns for non-uniform arrays are less well known, partly because the possibilities are so numerous and partly because the calculations, although straightforward, are rather tedious. Apparatus which would synthesize and display the pattern of any linear array antenna would greatly simplify the study of non'uniform arrays whether the non-uniformities are intentionally included in the design or are introduced inadvertently because of manufacturing inaccuracies.

2,874,381v Patented Feb. 17, 1959 Figure 2 is a block diagram of a preferred form of the invention; and

Figure 3 is a group of curves useful in explaining the invention. .L I

Referring first to Fig. l, there is show n diagrammatically a linear array antenna comprising a plurality of individual isotropicradiating elements 10, 11, 12, 13 etc. The distances of the elements 11, 12, 13 etc. from the first element 10 are denoted by s1, s2, s3 etc. Consider the field strength at any remote point P far enough from the array so that (1) the attenuation of the wave energy from each element is substantially the same and (2) lines drawn from each element to the point P are substantially parallel and make an angle 0 with the normal to the axis of the array. The total field strength will be the sum of the'contributions from each element and, neglecting attenuation, may be expressed as etc.

nein (www1-2i?? sin a) where ).:free space wavelength An object of this invention is to synthesize the radiation pattern of a linear array antenna.

Another object is to derive a voltage the time variations of which are analogous to the spatial variations of the power radiated by a linear array antenna.

Another object is to create a visual display which is analogous to the power radiated by a linear array antenna as a function of the angle of observation.

Briey stated, the invention comprises several variable frequency pulsed oscillators, one for each element vin the array to be synthesized. The relative starting times of the oscillators are individually adjustable. The output of each oscillator is split into an in-phase and a quadrature component. All of the in-phase components are added together and passed through a squaring circuit to derive a voltage proportional to thevsquare of the sum. Similarly, all of the quadrature components are added together and thensquared. The twosquared voltages are then added together andthe resulting voltage varies wthtime Ain a manner analogous to the way in which the power radiated by a linear array antenna varies with the angle of observation. The variations of the resulting voltagemay be displayed on an oscilloscope.

For a clearer understanding of the invention reference rnay be made to the following detailed description and the accompanying drawing in which:

" Figure l is a diagrammatic showing of the radiation of i" a linear array antenna;

6=angle of observation Equation 1 .can be expressed as thesummation of the typical terms and when Vso expressed becomes 71:, 218,. F(o)=21 Sm (m4-.M+ sm e (2) Equation 2 can be transformed by employing the trigonometric expression for the sine of the sum of two angles.

sin

cos wt sin (on-l- An` expression for the absolute value' of Equation 4 can be derived by the use of the trigonometric identity ,10 kc. p. s rto 40 kc. p. s.

, 3 'Equation l6, which expresses `the `iielcl strength as a function of 0, can be transformed to an analogue so as to .express field strength as afunction of time by means oftwo simplesubstitutions. rFirstylet Y 2 sin 6=pt (7) Second, note that pn represents a fixed angle and can be thought of as the rangle passed through in a xed period oftime tn. The angular velocity may be selected arbitrarily provided that tn is chosen accordingly. Therefore,let

Makin-gv nthese substitutions,'Equation 6 becomes A voltage the magnitude` of which varies with time in accordance withEquation 10 can be synthesized with the apparatus shown in.Fig..2.

Referring now to Fig. 2, there -is shown a timing wave generator 21 which may be a free running multivibrator. The .frequency is not critical but in `one particular embodiment is selected to be 1667 C. P. S. The generator 21 triggers a saw-tooth wave form generator 22 which, of course, will also have a frequency of 1667 C. P. S. The saw-tooth generator .should have a -linear rise in voltage for .arperiod of .approximately 120 microseconds but the recovery time is not critical since the rising portion of the wave .form is .the only ,portion .utilized and' is of much shorter duration than the period of the wave itself. This generator may, for example, be a phantastron circuit. The output of the generator 22 appears on conductor 23 so that'it may be led to several circuits each comprising a chain of components. The first chain comprises .a trigger generator` 24 the purpose of which is'to generate a short positive pulse atV a preselected time in each cycle. The generator 24 may, for example, comprise a blocking oscillator operation of which is inhibited until a control voltage has reached a predetermined magnitude. The control voltage in this case is the rising saw-tooth wave form'of generator 22 and the circuit lis arranged :to'initially'operate .the oscillator at any preselected interval of the rise-time of the sawtooth wave form. The "output pulse of the generator 24 is utilized to trigger a gate generator 25 which may comprise a multivibrator having a frequency of approximately 1000 C. P. S. so that a negative gate is generated for aiduration of approximately'SOO microseconds. This negative gate is led to a pulsed oscillator 2,6 so that oscillations are generated only during the period of the negative gate. The oscillator 26 should'be'adjustable in frequency and it may, for example, have a range of from The output of the oscillator 26 is controlled .in magnitude'by potentiometer 27 the slider of which is connected to two additionalpotentiometers 28 and 29 so that there are available two outputs the amplitudes of which may be adjustedsimultaneously by the potentiometer 27 and individually by the potentiometers 28 and 29. The slider of the potentiometer 28 is connected to aconductor 31 which, as will be more 4fully explained, has a potential thereon which may be represented by the expression I1 sin p1(t1+t). The

fslider of potentiometer 29 is connected to a phase shifting circuit 32 the purpose of which is to provide lan output in quadrature with the voltage on conductor 31. The phase shifter 32 may 'comprise an amplifier and a Miller integrator, and the output on conductor 33 may be represented by the expression I1 cos p1(t1}t).

Additional chains of components similar to that just described are also connected to vconductor 23. One of these is shown and comprises a trigger'generator 36, a gate generator 37, a pulsed oscillator 38potentiometers 41, 42 and 43, anda phase shifter 44. Additional chains of components are represented by the dashed lines such as 45 and 46.

The output of all of kthe potentiometers such as 28 and 42, representing as they do sine functions, are led to an adding circuit 51 which derives an output proportional to the sum of the input voltages. The adding circuit may comprise a conventional parallel .resistive adding network. Similarly, the. outputs of the phase Shifters such as 32 and 44, representing cosine functions, are led to. an .adding circuit 52 which may be identical to circuit 51 and which Yderives an output proportional to the sum jof all of the inputs. The outputs of ,adding circuits of 51 and 52 are led to squaring circuits 53 and v54 respectively the purpose of each of'which is to derive an output voltage the magnitude of which is proportional to the square .of theV input voltage. Each of the circuits '53 and 54'is preferably an electronic circuit comprising push-pull electronic tubes. The outputs of the two squaring circuits `53* and 54 are next .added together by 'means of an adding circuit 55 which may also comprise ka parallel resistor adding network. The sum voltage from the adding circuit 55 .is led to the vertical deflection systemV of an oscilloscope 56, the horizontal sweep circuit kof which Ais synchronized by the timing wavegenerator21.

The output of the adding Vcircuit'SS is a voltage the magnitude of which is proportional .to the square of .the eld strength of the radiation pattern of the simulated linear arrayas can be seen'by referring back to Equation l0. The oscillator 26 'generates a voltage ofy the form I1 sin plt. The initial phase of the oscillation is controlled by the starting time of .the negative gate ,generated by thejgate'generator 25 which thereby alters the output so as to be of theform Ilsin plm-let). The magnitude of this *voltage which is analogous to I1 may be adjusted by means of the potentiometer 27. The remaining chains of components generate similar voltages corresponding to lzsin. @U2-let), I3 sin p3(t3+t)A etc. The phase VShifters 32, 4.4, etc. derive voltages `which correspondto the terms l1 cosV g1(t1-{-t),-l2 cos p2(t2+t), 1.3 cos.p(t3.t.) etc. .All of the sine functions are collectedand added bythe adding circuitVSl and are squared by the 'circuit 53. Similarly, all of cosine functions are collected and added'by the adding circuitSZ and squared 'in the circuitV 54. The squares are then added 'together in the 4circuit 55. LThe resulting voltage then is seen to correspond in Vform to the .function of Equation 10.

Yfigures' is an aid to understanding the invention. Reference Icharacter'61 denotes the wave 'form of the output 65 'of the timing wave generator 21 having a frequency of 1667 C. P. S. and 'aperiod of 600 psec. 'The positive going portion triggers the saw-tooth generator 22 which generates a .linear rising voltage waveform 62 .having a duration of approximately aseo. An early ,portion of the wave lform 62, for example 10 nsec. from the start, is selected as areference Vtime to from which the remaining time intervalsztbftz, t3 etc. aremeasured. Aspreviouslymentioned, the trigger generator 24 emits a pulse when the impressed voltage (wave 62) .has reached a predetermined level. Thus a simple voltage 'generate pulses at the appropriate times.

The adjustment of the frequencies of the oscillators and the time intervals t1, t2 etc. can best be understood by considering an example. Suppose it is required to simulate a six element linear array having the followingspacings, phases, and relative illuminations:

Table I Elment; 1 2 a 4 '5 c spaeing .5A .7A 1.4A 2.0). aoA Phase (d +30 en 18o +90 -90 -235 mummanon 1 1.5 2.o 2.o 1.5 1.o

4First consider. the spacing. Itv will be recalled from Equation 7 :that

" sin 0 Pnt:

and this relationshiplcan be expressed in the form of `two equations, thus:

The angular velocities p1, p2 etc. `(and thefrequencies) are therefore seen to be directly proportional to the spacing. The first element has zero `spacing from itself and it would appear to be necessary to make the frequency of oscillator V26 zero.A In order to avoid this situation a fictitious elementLcalled the zero order or zeroeth element, is assumedto be positioned before the first element at any arbitrarily selected distance. It is convenient to assume this distance to be 1.0A. The spacings ofthe remaining elements from the zeroeth element ytliusare 1.0A, 1.'5A, 1*.7A, 2.4A, 3.0A and 4.0A respectively. `'I'he frequency for one of the Aoscillators may now be chosen arbitrarily and if wefchoose the frequency' of oscillator 26 to be 10 kc. p. s. we note that 10 kc. p. s. corresponds to a spacing of one wavelength and the frequencies of the remaining oscillators will be 15, 17, 24, 30 and 40-kilocycle's respectively.

"Considernow thephase of the energy emitted'by the individual radiating elements and the selection'of the `correspondingtime `intervals lt1, t2 etc. It is Yconvenient pto' regard the element havingthe greatest leadA` as -the'v reference element and to regard the remaining elements on lagging that element in phase. Since in this case element 4 has the greatest lead this element will be regarded as the reference element having zero `phase and the phase of the elements1-6 with respect to element 4 then become -60, -150, 2702 0', -180 and -325 respectively. It will be recalled from Equation 8 where Tn is the period ofthe nth oscillator in seconds,

tn is the time delay in seconds, and qsn is the phase anglev in radians. Forthe oscillator 26' the frequency of which 6 is l0 kc. p. s., the period is 10Q ,n.sec. andthe time interval t in 1 s60 The time interval X 100= 16.7 sec.

The remaining intervals t3-t6 are similarly computed and are found to be 43.4, 0, 16.7 and 22.6 microseconds respectively. Table-II below summarizes the above cornputations.

Table Il Element .0 1 V2 3 4 5 6 Spacing from No. 1 0 6A 7A l. 4A 2. 0A 3. 0A Spacing from N o. 0 l 0A l. 5A 1. 7A 2. 4A 3. 0A 4. 0A Frequency (kc)- 0 15 17 24 30 40 Period (n sec.) 58. 8 41. 7 33. 3 25 Phase (degrees -180 +90 -90 V235 Adjusted Phas -270 0 -180 -325 Time (n sed). 43. 4 O 16. 7 22. 6 Illuminatlon 2. 0 2.0 1. 5 1.0

To set up the apparatus to display the pattern of the above discussed'array, computations such as shown in Table II are first made. Next the apparatus is turned on and the amplitude and duration of the linear portion of the sawtooth wave are measured. Thus a linear relation between voltage and time is` established. Next the fourth trigger generator is adjusted so that a pulse Ais generated when the voltage of the sawtooth wave'has risen tothe point marked to in Fig. 3. If the trigger generator is a. blocking oscillator this adjustment may be made by setting the reference voltage level with an internal potentiometer. Next the reference voltage levels Y of the remaining trigger generators are adjusted so that pulses are generated atrthe proper times as shown in Table Il. Y 1 j The frequency of the oscillator 26 should next be adjusted' `to thevalve shown byk Table Il, that is, l0 kc. p. ls. This adjustment can be made by comparing the output of oscillator 25 with the output of an adjustable standard reference oscillator, preferably using an oscilloscope to make the comparison. After the frequency has been' set, the voltages of conductors 31 and 33 should be made equal by adjusting the potentiometers 28 and 29. The remaining oscillators are ladjusted in the same manner. l

-The illumination may be adjusted to the relative values` indicated in'Table II by means of the'potentiometers potentiometers in each of `the remain- 27', 41, and like ing circuits. l vvThe sweep lcircuit of the oscilloscope 56 should be adjusted to`have a rise time of just under 600 microseconds, as shown by the curve 67 of Fig. 3, so that it can be synchronized by the positive` going portion' of the wave form 61 from the timing pulse generator 21. On the oscilloscope screen vthe abscissal is, of course, time but is directly proportional to sin 0 and the factor Aof proportionality can be found Vfrom Equations ll and 12. In the example being considered a spacing of 1.0A corresponds to a frequency of l0 kc. p. s. From Equation l2 k is found to be equal to 100 microseconds. Equation .l1 shows that 10() microseconds corresponds to ninety degrees of variation of 0, so that 400 microseconds corresponds to 360 variation of 0.

From the foregoing description Yit is seen that the present invention provides apparatus bymeans of which the radiation pattern of virtually any linear array antenna may be synthesized and visually displayed. The

spacing between radiators, the phase of the energy emitted by each radiator, andthe relative magnitude of the illumination may be individually adjusted and need not Vvary uniformly from radiator to radiator.

What is claimed is:

1. An antenna pattern synthesizer comprising, a plurality of variable frequency oscillators, means for repeatedly starting and stopping the'generation of oscillations, means for deriving from the output of each of said oscillators first and second voltage components in quadrature with each other, means for adding all of said first components together to obtain a first summation voltage, means for adding all of said second components together to obtain a second summation voltage, means for deriving a first squared Voltage proportional to the square of said first summation voltage, means for deriving a second squared voltage proportional to the square of said second summation voltage, and means for adding said rst and secondsquared voltages to obtain a resulting voltage the amplitude variations of which as a function of ltime are analogous to the variations in the power radiated by an antenna as a function of the angle of observation.

y2. An antenna pattern synthesizer comprising, a plurality of variable frequency oscillators, a timing wave generator, means controlled by said timing wave generator for repeatedly starting and stopping the operation of said oscillators, means for deriving from the output of each of said oscillators first and lsecond voltage come ponents in quadrature with each other, means for adding all of said first components together to obtain a first summation voltage, means for adding all oi said second components together to obtain a second summation voltage, means for deriving a rst squared voltage proportional to the square of said first summationv voltage, means for deriving a second squared voltage proportional to the square of said second summation voltage, means foradding said first and second squared voltages to obtain a resulting voltage, and means' controlled by said timing wave generator for visually displaying the amplitade of said resulting voltage'as a function of time.

3. An antenna pattern synthesizer comprising, a plureality of variable frequency oscillators, a timing wave generatonmeans controlled by said timing wave genera-v tor for repeatedly starting and stopping the operation of said oscillators, said means including means for adjusting the relative times at which the generation of oscillay tions is started in each of said oscillators, means for adding together the voltage outputs of all of said oscillators ,to obtain l.a first voltage,l means for deriving a Vsecond voltage lproportional to the square of said Iirst voltage, means for deriving a plurality of voltages each in quadrature with the voltage output of one of said oscillators, means for adding together all of said quadrature voltages toobtain ka-third voltage, means for deriving a fourth voltage proportional to the square of said third-voltage,

meanswfor adding together said second and fourth voltages to obtaina'vfifth voltage, an oscilloscope,` means for applying said fifth voltage to the vertical deflection sys` tem of said oscilloscope, and means for controlling the @einer horizontal ldefleoton ,systonof Said oscilloscope by .said timing wave generator.

.4. .A n antenna pattern synthesizer oomprisiins; a pl11 rfality of variable 'frequency oscillators, a timing wave generator, means controlled by said timing wave generatorfor repeatedly starting and stopping the operation of all of v,said oscillators, said means including means Vfor varying the relative times at which the generation of oscillations is initiated by each of said oscillators, means for individually varying the magnitude of the output of said oscillators, means forderiving from the output of each of said oscillators first and second voltage components inquadrature with each other, means for adding all ofsaid firstk components together to obtain a first summation voltage, means for .adding all of said' second components together to obtain a second summation voltage, means for deriving a first squared voltage proportional to the square of said first summation voltage, means for deriving asecond squared voltage proportional to the square of said second summation voltage, means for adding said first andsecond squared voltages to obtain a resulting voltage, and means'controlled by said timing wave generator for visually displaying the amplitude of said resulting voltage as a function of time.

5. An antenna pattern synthesizer comprising, a plurality of variable frequency oscillators, a timing wave generator, means vcontrolled by said timing wave generator for repeatedly starting and stopping the operation of all of said oscillators, said means including means for varyingthe relative times at which the generation of oscil- .lations is initiated by each of said oscillators,jmeans `for individually varying the magnitude of the output of said oscillators, means for deriving from the output of each of said oscillators first and second voltage components equal in magnitude and in phase quadrature with each other, means for adding all of said first components t0- gether toy obtain a first summation voltage, means for adding yall of said second components together to obtain a secondtsummation voltage, means for deriving a first squared voltage proportional to the square ofsaid first summation voltage, means for-deriving a second squared voltage proportional to the square of said second summation voltage, means for adding said first and second ksquared voltages to 'obtain a vresulting voltage, an oscilloscope, means for applying said resulting voltage to the rvertical defiection system of said oscilloscope, and means for controlling the horizontal deection system of said oscilloscope by said timing wave generator.

References Cited in the lille of this patent l UNITED yPATENTS 2,457,790 wird et a1. Dec. 2s., 1948 2,568,927 Morrison Sept. 25., 1951 2,684,467 'Young et al- Ju1yf20, 19.54

. Fisk et al. Apr. 5, 1955 

